Optical interferometry is used to make precise measurements in a variety of settings. For example, semiconductor lithography systems use laser interferometry to measure displacements and accurately position stages to nanometer precision. In these systems a laser beam (sometimes referred to as a test beam or measurement beam) aligned to the cavity motion is reflected off a mirror attached to the moving object and is interfered with another beam that serves as a reference. The interference phase changes by 2π each time the beam path changes by a wavelength, so the interference phase provides a measurement of changes in the cavity length. Heterodyne or homodyne techniques may be used to extract the phase of the interference.
Often in these systems the test light beam travels long distances in air. If the refractive index of the air in the beam path changes, even locally, the change manifests itself as an apparent displacement of the object being measured. This apparent displacement constitutes a measurement error and the longer the air path, the more serious this error is likely to be.
A class of displacement measurement interferometers with significantly shorter beam paths through includes interferometric encoder systems. Typically, an interferometric encoder system includes a periodic structure known as an encoder scale (e.g., a grating) and an encoder head. The encoder head is an assembly that includes an interferometer. The interferometer directs a test beam to the encoder scale, where it diffracts. The interferometer combines the diffracted test beam with a reference beam to form an interfering output beam whose interference phase is related to the optical phase difference between the two beams. Interferometric encoder systems measure displacement that is transverse to the test beam by measuring the phase shift of a beam reflected off of the encoder scale. As the patterned surface of the encoder scale moves under the test beam, the phase of the test beam relative to a fixed reference beam after reflecting off the encoder shifts by 2π for each pattern period. High precision measurements of the beam phase then allow displacement measurements to small fractions of a pattern period. Since the measured motion of the encoder scale is transverse to the test beam, significant reduction in the cavity length and hence the beam air path may be achieved, thereby minimizing atmospheric refractive index fluctuations.